MANCHESTER, New Hampshire (CNN) -- Republican presidential candidates directed as much of their firepower at President Bush as they did at each other in Tuesday night's debate.

The debate at Saint Anselm College was the party's first in New Hampshire, which hosts the nation's first primary early next year. CNN senior political analyst Bill Schneider said the debate differed from that of the Democrats on Sunday.

"Republicans clearly decided not to look like squabbling Democrats and to concentrate their fire on Democrats -- and to a surprising extent, on President Bush: the mismanagement of the war, the spending, the immigration bill," Schneider said.

During the first half of the two-hour event, journalists from the debate's sponsors -- CNN, WMUR-TV and the New Hampshire Union Leader -- asked candidates questions about Iraq, energy, oil policy and immigration.

Answering an opening query on the Iraq war, most candidates defended the 2003 invasion and supported a continued U.S. commitment, but expressed some criticism of the Bush administration's handling of the war.

The second half of the debate allowed the audience to pose questions.

One audience member, Erin Flanagan, her voice cracking with emotion, said her brother died fighting in Iraq. She asked for the candidates' Iraq exit strategies and how they would quell violence there.

Sen. John McCain of Arizona walked to the edge of the stage and looked at Flanagan. "I'm going to give you a little straight talk. This war was very badly mismanaged for a long time," he said. (Watch McCain take shot at Clinton over Iraq)

Former Massachusetts Gov. Mitt Romney fielded a question earlier in the debate about whether the Iraq war was a mistake.

"We knew what we knew at the point we made the decision to get in," said Romney. "At this stage the right thing is to see if we can stabilize the central government." (Watch Romney discuss his Mormon faith)

And Kansas Sen. Sam Brownback said he supports breaking Iraq up into Kurdish, Shiite Arab and Sunni Arab regions to head off further bloodshed.

Schneider said McCain's performance reminded New Hampshire voters of why they backed him in their 2000 primary.

"Even on issues where most Republicans disagree with him, like immigration, McCain made his case boldly and honestly," Schneider said.

The candidates' responses clarified the central issue for the 2008 general election campaign, Schneider said.

"Republicans will argue that leaving Iraq too soon will increase the threat of terrorism in the United States. Democrats will argue exactly the opposite -- that staying in Iraq increases the terrorist threat," he said.

But on Tuesday night, no candidate was running on the legacy of the Bush administration.

Rep. Tom Tancredo of Colorado said White House political adviser Karl Rove called him in 2003 and told him that "because of my criticism of the president, I should never darken the doorstep of the White House."

Tancredo said he is "so disappointed" in the president that, if elected, he "would have to tell George Bush exactly the same thing Karl Rove told me."

"We've got to completely transform the health care system, make it a wellness system and make it a prevention system," he said.

There are 125 million Americans who have at least one chronic illness, he said.

But it was another Thompson whose shadow loomed over the debate -- actor and former Sen. Fred Thompson is already raising money and advisers say it's very likely he will formally join the race in early July.

An average of the latest national polls shows Giuliani leading the race, with about 30 percent support, followed by McCain at 22 percent, Fred Thompson at 12 percent and Romney at 10 percent. The rest of the announced candidates each came in at 2 percent or less.